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Splitting (novel)
Splitting may refer to: * Splitting (psychology) * Lumpers and splitters, in classification or taxonomy * Wood splitting * Tongue splitting * Splitting (raylway), Splitting, railway operation Mathematics * Heegaard splitting * Splitting field * Splitting principle * Splitting theorem * Splitting lemma * for the numerical method to solve differential equations, see Symplectic integrator See also * Split (other) * Splitter (other) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Splitting (psychology)
Splitting, also called binary thinking, dichotomous thinking, black-and-white thinking, all-or-nothing thinking, or thinking in extremes, is the failure in a person's thinking to bring together the dichotomy of both perceived positive and negative qualities of something into a cohesive, realistic whole. It is a common defense mechanism, wherein the individual tends to think in extremes (e.g., an individual's actions and motivations are ''all'' good or ''all'' bad with no middle ground). This kind of dichotomous interpretation is contrasted by an acknowledgement of certain nuances known as "shades of gray". Splitting can include different contexts, as individuals who use this defense mechanism may "split" representations of their own mind, of their own personality, and of others. Splitting is observed in Cluster B personality disorders such as borderline personality disorder and narcissistic personality disorder, as well as schizophrenia and depression. In dissociative identity ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lumpers And Splitters
Lumpers and splitters are opposing factions in any academic discipline that has to place individual examples into rigorously defined categories. The lumper–splitter problem occurs when there is the desire to create classifications and assign examples to them, for example, schools of literature, biological taxa, and so on. A "lumper" is a person who assigns examples broadly, judging that differences are not as important as signature similarities. A "splitter" makes precise definitions, and creates new categories to classify samples that differ in key ways. Origin of the terms The earliest known use of these terms was thought to be Charles Darwin, in a letter to Joseph Dalton Hooker in 1857: "It is good to have hair-splitters & lumpers". But according to research done by the deputy director at NCSE, Glenn Branch, the credit is due to naturalist Edward Newman who wrote in 1845, "The time has arrived for discarding imaginary species, and the duty of doing this is as imperative ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wood Splitting
Wood splitting (''riving'',"Riving" def. 1.b. ''Oxford English Dictionary'' Second Edition on CD-ROM (v. 4.0) Oxford University Press 2009 cleaving) is an ancient technique used in carpentry to make lumber for making wooden objects, some basket weaving, and to make firewood. Unlike sawmill, wood sawing, the wood is split along the Wood grain, grain using tools such as a hammer and Wedge (mechanical device), wedges, splitting maul, cleaving axe, side knife, or froe. Woodworking In woodworking carpenters use a wooden siding which gets its name, clapboard, from originally being split from logs—the sound of the plank against the log being a clap. This is used in Clapboard (architecture), clapboard architecture and for Panelling#Wainscot_panelling, wainscoting. Coopers use oak clapboards to make barrel staves. Split-rail fences are made with split wood. Basket making Some Native Americans traditionally make baskets from Fraxinus nigra, black ash by pounding the wood with a mallet a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tongue Splitting
Tongue bifurcation, splitting or forking, is a type of body modification in which the tongue is cut centrally from its tip to as far back as the underside base, forking the end. Bifid tongue in humans may also be an unintended complication of tongue piercingsFleming, P., Flood, T. Bifid tongue — a complication of tongue piercing. Br Dent J 198, 265–266 (2005). https://doi.org/10.1038/sj.bdj.4812117 or a rare congenital malformation associated with maternal diabetes, orofaciodigital syndrome 1, Ellis–Van Creveld syndrome, Goldenhar syndrome, and Klippel–Feil syndrome. Practice Deliberate tongue splitting is a cosmetic body modification procedure that results in a ‘lizard-like’ bifid tongue. Tongue bifurcation has also been reported as an unintended complication of tongue piercing. Process Tongue bifurcation may be done surgically using a scalpel, or cauterised with a laser. It is performed by oral surgeons, plastic surgeons, or body modification practition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Splitting (raylway)
Splitting may refer to: * Splitting (psychology) * Lumpers and splitters, in classification or taxonomy * Wood splitting * Tongue splitting * Splitting, railway operation Mathematics * Heegaard splitting * Splitting field * Splitting principle * Splitting theorem * Splitting lemma * for the numerical method to solve differential equations, see Symplectic integrator In mathematics, a symplectic integrator (SI) is a Numerical ordinary differential equations, numerical integration scheme for Hamiltonian systems. Symplectic integrators form the subclass of geometric integrators which, by definition, are canonical ... See also * Split (other) * Splitter (other) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heegaard Splitting
In the mathematical field of geometric topology, a Heegaard splitting () is a decomposition of a compact oriented 3-manifold that results from dividing it into two handlebodies. Definitions Let ''V'' and ''W'' be handlebodies of genus ''g'', and let ƒ be an orientation reversing homeomorphism from the boundary of ''V'' to the boundary of ''W''. By gluing ''V'' to ''W'' along ƒ we obtain the compact oriented 3-manifold : M = V \cup_f W. Every closed, orientable three-manifold may be so obtained; this follows from deep results on the triangulability of three-manifolds due to Moise. This contrasts strongly with higher-dimensional manifolds which need not admit smooth or piecewise linear structures. Assuming smoothness the existence of a Heegaard splitting also follows from the work of Smale about handle decompositions from Morse theory. The decomposition of ''M'' into two handlebodies is called a Heegaard splitting, and their common boundary ''H'' is called the Heegaard su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Splitting Field
In abstract algebra, a splitting field of a polynomial with coefficients in a field is the smallest field extension of that field over which the polynomial ''splits'', i.e., decomposes into linear factors. Definition A splitting field of a polynomial ''p''(''X'') over a field ''K'' is a field extension ''L'' of ''K'' over which ''p'' factors into linear factors :p(X) = c \prod_^ (X - a_i) where c \in K and for each i we have X - a_i \in L /math> with ''ai'' not necessarily distinct and such that the roots ''ai'' generate ''L'' over ''K''. The extension ''L'' is then an extension of minimal degree over ''K'' in which ''p'' splits. It can be shown that such splitting fields exist and are unique up to isomorphism. The amount of freedom in that isomorphism is known as the Galois group of ''p'' (if we assume it is separable). A splitting field of a set ''P'' of polynomials is the smallest field over which each of the polynomials in ''P'' splits. Properties An extension ''L'' th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Splitting Principle
In mathematics, the splitting principle is a technique used to reduce questions about vector bundles to the case of line bundles. In the theory of vector bundles, one often wishes to simplify computations, for example of Chern classes. Often computations are well understood for line bundles and for direct sums of line bundles. Then the splitting principle can be quite useful. Statement One version of the splitting principle is captured in the following theorem. This theorem holds for complex vector bundles and cohomology with integer coefficients. It also holds for real vector bundles and cohomology with \mathbb_2 coefficients. In the complex case, the line bundles L_i or their first characteristic classes are called Chern roots. Another version of the splitting principle concerns real vector bundles and their complexifications: Consequences The fact that p^*\colon H^*(X)\rightarrow H^*(Y) is injective means that any equation which holds in H^*(Y) — for example, among ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Splitting Theorem
In the mathematical field of differential geometry, there are various splitting theorems on when a pseudo-Riemannian manifold can be given as a metric product. The best-known is the Cheeger–Gromoll splitting theorem for Riemannian manifolds, although there has also been research into splitting of Lorentzian manifolds. Cheeger and Gromoll's Riemannian splitting theorem Any connected Riemannian manifold has an underlying metric space structure, and this allows the definition of a ''geodesic line'' as a map such that the distance from to equals for arbitrary and . This is to say that the restriction of to any bounded interval is a curve of minimal length that connects its endpoints. In 1971, Jeff Cheeger and Detlef Gromoll proved that if a geodesically complete and connected Riemannian manifold of nonnegative Ricci curvature contains any geodesic line, then it must split isometrically as the product of a complete Riemannian manifold with . The proof was later simplified by J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Splitting Lemma
In mathematics, and more specifically in homological algebra, the splitting lemma states that in any abelian category, the following statements are equivalent for a short exact sequence : 0 \longrightarrow A \mathrel B \mathrel C \longrightarrow 0. If any of these statements holds, the sequence is called a split exact sequence, and the sequence is said to ''split''. In the above short exact sequence, where the sequence splits, it allows one to refine the first isomorphism theorem, which states that: : (i.e., isomorphic to the coimage of or cokernel of ) to: : where the first isomorphism theorem is then just the projection onto . It is a categorical generalization of the rank–nullity theorem (in the form in linear algebra Linear algebra is the branch of mathematics concerning linear equations such as :a_1x_1+\cdots +a_nx_n=b, linear maps such as :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matrix (mathemat . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symplectic Integrator
In mathematics, a symplectic integrator (SI) is a Numerical ordinary differential equations, numerical integration scheme for Hamiltonian systems. Symplectic integrators form the subclass of geometric integrators which, by definition, are canonical transformations. They are widely used in nonlinear dynamics, molecular dynamics, discrete element methods, particle accelerator, accelerator physics, plasma physics, quantum physics, and celestial mechanics. Introduction Symplectic integrators are designed for the numerical solution of Hamilton's equations, which read \dot p = -\frac \quad\mbox\quad \dot q = \frac, where q denotes the position coordinates, p the momentum coordinates, and H is the Hamiltonian. The set of position and momentum coordinates (q,p) are called canonical coordinates. (See Hamiltonian mechanics for more background.) The time evolution of Hamilton's equations is a symplectomorphism, meaning that it conserves the symplectic 2-form dp \wedge dq. A numerical sche ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
